Wednesday, 14 March 2012

Higgs or BEEEH boson?

during the session featuring the latest experimental results on the Higgs boson searches the name Higgs did not appear at all. Instead, the speakers were discussing a mysterious SM scalar boson (?) or on a BEEEH boson (???), the latter name apparently inspired by a herd of sheep grazing outside the conference room. The most logical explanation is that the Moriond attendants have been collectively hypnotized and conditioned to say BEEEH every time they meant Higgs (I saw a similar trick at a hypnosis show in Las Vegas). That theory would also explain why only the strongest characters continued referring to the Higgs. The alternative explanation -- that someone at the conference had an idea to rename the Higgs boson into a BEEEH boson and talked to it so many otherwise reasonable scientists -- sounds utterly implausible. That's because the idea

is obviously silly,

betrays ignorance.

I guess there's no need to elaborate too long on why it's silly. In physics and mathematics communication heavily relies on established conventions. Like, we all agree the result of adding 2 and 2 should be called 4, although there is no deep reason for it; we could call 11 or 666 depending on the moon phase, and that would be perfectly consistent as long as we were careful to preserve the axioms of the addition group. However calling it 4 at all times makes our life easier and helps avoiding confusion. By similarly established conventions, spontaneous breaking of a local symmetry in a quantum field theory is referred to (somewhat unfairly) as the Higgs mechanism, while a spin-0 particle excitation often associated with that breaking is called (deservedly) the Higgs boson. This is how it's been for the last 40 years and this is how it'll remain.

The ignorance count deserves a bit longer explanation, as it is related to a misunderstanding that is not so uncommon. The main point is that one should clearly distinguish the Higgs mechanism from the Higgs boson; the two are often intricately related but formally they are distinct concepts, in particular the former may well exist without the latter.

The Higgs mechanism, or spontaneous gauge symmetry breaking, occurs when a Lorentz-invariant Lagrangian is also invariant under a local symmetry group with the corresponding set of gauge bosons, however some or all of these gauge bosons are massive. Such a theory still obeys a local symmetry, albeit non-linearly realized. We can describe it in a gauge invariant way with the help of a set of unphysical scalar particles called the Goldstone bosons who have a derivative mixing with the massive gauge bosons. For the public, we say that each massive gauge boson eats a Goldstone boson so as to acquire mass and another internal degree of freedom associated with it. For example, the W and Z boson must eat a triplet of Goldstone bosons. The ensemble of these phenomena is referred to as the Higgs mechanism, although more properly it should be called the Anderson-Nambu mechanism (who grasped the general idea, inspired by the related phenomenon of superconductivity in condensed matter physics), or the Brout-Englert-Higgs mechanism (who first understood its workings in the context of Lorentz invariant quantum field theories). However, the name of Higgs somehow stuck, probably because it's cute, or maybe because we all hate Anderson for cutting the throat of the SSC.

One important point is that a confirmation of the Higgs mechanism is not what the LHC is now after. Indeed, the fact that the fundamental interactions obey to a very good precision the local SU(2)xU(1) symmetry which is spontaneously broken to the electromagnetic U(1) was firmly established by the LEP experiment back in the 90s.

The LHC is now after the Higgs boson, which is something else. It turns out that in spontaneously broken gauge theories certain amplitudes, in particular those of the massive gauge bosons, grow with the center-of-mass energy. As a consequence, the theory cannot remain perturbative up to an arbitrarily high energy scale. In the Standard Model without the Higgs boson the loss of perturbativity would happen already at 1 TeV. Thus, there must be something that regulates the high-energy behavior of the W and Z scattering amplitudes. Out of several possibilities, the simplest one is to introduce an isospin-0 scalar resonance with the coupling to the W and Z bosons proportional to their masses. Voila the Higgs boson. It's not a unique possibility, but it's the one that is clearly favored by current experimental data.

Now, the Higgs boson first appeared in the paper of, surprise, Higgs in 1964, while it was completely missed in the earlier paper of Brout and Englert, and swept under the carpet in the paper by Guralnik, Hagen, and Kibble. In fact, the importance of that degree of freedom was not realized until a few years later, thanks to the papers of Higgs and Kibble, and ultimately thanks to papa Weinberg who incorporated it in the Standard Model in 1967.

In summary, if you hear someone speaking about the Brout-Englert-Higgs mechanism, that's fine, he's just trying to be fancy (and has a grudge against condensed matter). However, if you hear him talking about the BEEEH boson, that not only sounds funny but is also a good indicator that he has little idea about the subject.

Update: I see that I should clarify that this post is not about who should get the Nobel prize; that's a longer discussion. I just think that both esthetic reasons and historical truth dictate that we should continue to call the particle the Higgs boson.

68 comments:

Anonymous
said...

The spirit of this is correct as "BEH Boson" is silly and revises history. Brout and Englert did not have the boson.

However the comment on GHK is not fully correct - they had the boson and explicitly showed how the Goldstone theorem and is avoided. That said, GHK did focus more on the Goldstone theorem rather than the boson.

The point is that unlike the Goldstone boson, which is still present but not discussed (and remains a problem) in Higgs' approach to the theory, the "Higgs boson" has no intrinsic theoretical constraint on its mass and indeed this mass cannot be calculated because of the fundamental limitations of quantum field theory. This is why the experimentalists did not know for sure where to look for the particle.

In the lowest approximation, the GHK mass of the boson is zero (see p. 586 of GHK paper). In Higgs' lowest approximation (which is different from GHK but leads to the same final theory) it can be set (but is not) to any value including zero because he does not set a parameter which is irrelevant to the actual final value of the mass.

Also (depending on what you mean) it was not Higgs and Kibble that addressed the "degrees of freedom in 1967" - that was flushed out in GHK paper in showing how the boson got mass and avoided the Goldstone theorem. See below for further details.

http://arxiv.org/abs/1110.2253

http://arxiv.org/abs/0907.3466

Unless you mean something different by that that phrases but it was not address in the 1967 papers.

It's funny how history gets revised so easily, without a smudge of concern... Firstly, it's not been 40 years that the boson has been referred to as "Higgs", this happened later. See, for example, Spontaneous Breakdown of Symmetry in Axiomatic Theory (sections 3 and specially 4). Secondly, i've always found all this story about non-linear realizations of symmetries super funny: what's so hard about promoting a global to a local (gauge) symmetry? Or representing 'G/H' appropriately? The point is that what's in question here is less about how a symmetry gets realized and more about how differential eqs are solved: not all solutions of a diff eq need to share the symmetry of its parent eq. Thirdly, Anderson did little to this subject, other than to mention his insights from condensed matter. Now, one must notice the difference between condensed matter systems and high energy ones: Lorentz symmetry. Life is very different when you have to deal with Lorentz symmetry. You should ask R.V. Lange (1965, 1966), who proved the condensed matter analogue. Finally, as for your opinion on the three seminal papers, the commenters above already did a good job explaining some of the details, but you may also enjoy reading the following: Gauge Invariance and the Goldstone Theorem.

These are interesting thoughts and relevant historical facts (and non-facts) and whether the actual boson was mentioned by some of the physicists may be relevant.

Or not.

It doesn't have to be relevant. The actual boson is really a big piece of evidence that the mechanism of spontaneous symmetry breaking is right as an explanation of the masses of W,Z bosons etc. The boson is a part of the same package of insights and for the sake of simplicity, I think it's natural to have the same name for both even if some of the physicists didn't explicitly mention the boson.

Those thoughts are theoretical in character because I would have trouble to relearn not to say "Higgs boson" myself. But I surely do agree that Peter Higgs' importance is being overstated relatively to others. He's a nice guy (and I shared an office in Santa Barbara with him once) but it's clear that Englert etc. are at least in the same league while the fog caused by the Higgs terminology creates a very different impression.

Also, whatever criticism one may direct against Anderson, I think that it's inevitable for fairness to admit that this is a topic in which wisdom was being imported from condensed matter physics. Condensed materials are never Lorentz-invariant, they always pick a preferred frame, the rest frame. But one really gains the Lorentz invariance automatically if the idea is imported to particle physics in the most straightforward way so one shouldn't sell this Lorentz symmetry as an incredible achievement or deep insight by a HEP physicist.

Landau-Anderson-BEH-GHK boson/mechanism etc. may be too long and inconvenient but it's still true that it could be more fair. At the end, people could agree that the God particle is a great and practical terminology.

Just to say, one can not break spontaneously a gauge (i.e. local) symetry, as it is not a physical symetry (it is a redundance of the physical content of the theory). If it was the case, it would be really bad, the theory being spoiled because different field configurations would not be equivalent anymore but still supposed representing the same physical state.

What you can spontaneously break is a global symetry. And this is what you do when the higgs gets a non-zero vev. Then the global SU(2)xU(1) is broken to U(1) (and if you do a global transformation on the field, you will have a different physical state (not the same vev)) whereas the gauge (local) SU(2)xU(1) symetry is unbroken (and if you do a gauge transformation, the state is still the same, as it should).

This is subtile point which is usually overlooked, especially in condensed matter where people use the term gauge symetry for global symetry...

What was the first paper to mention the modern point of view, which is that you don't need any explanation of why the Goldstone theorem is avoided because there was never a symmetry there to begin with? A gauge symmetry mods out by the symmetry, so all the different states that would presumably be connected by the Goldstone mode are in fact a single state. There is nothing to explain.

"We can describe it in a gauge invariant way with the help of a set of unphysical scalar particles called the Goldstone bosons who have a derivative mixing with the massive gauge bosons. For the public, we say that each massive gauge boson eats a Goldstone boson so as to acquire mass and another internal degree of freedom associated with it. For example, the W and Z boson must eat a triplet of Goldstone bosons. The ensemble of these phenomena is referred to as the Higgs mechanism..."

Is this a just-so story?

Or is it supposed to have something to do with the physical world we live in?

Jester - I will try to explain this simply and outline what you are missing.

It is indeed correct that the "Higgs boson" is massless in the GHK paper. The point is that this masslessness has nothing to do with the Goldstone theorem or any other constraint on the theory. Getting around the Goldstone theorem is the entire point of these 1964 PRL papers. If the constraints of the theorem were valid, there would be a required massless scalar particle which was not and is not observed in nature. In this model, GHK starts with a massless two degree of freedom vector particle and two massless (one degree of freedom) scalar particles.

GHK makes an approximation: The massless non-higgs scalar degree of freedom combines with the two degrees of freedom of the massless vector particle to make a vector particle with 3 degrees of freedom and which has mass. Nothing happens to the other scalar degree of freedom which remains massles and is the "Higgs Boson". This is clear in the GHK paper because it is stripped down to only physical degrees of freedom by its choice of gauge (radiation).

To repeat, GHK picked a model which initially has no interaction with the scalars amongst themselves and also picked a leading order approximation that is consistent with all the symmetries of the model. This approximation leaves the boson degree of freedom associated with the "Higgs Boson" massless. In this order, no interaction between this degree of freedom and the vector field is visible and hence it is decoupled. Similarly, in Dr. Higgs's model his boson is decoupled in his approximation. This is no surprise, either of these models and the approximation studied ends up looking like free fields. In particular a free massive vector field and free massless higgs boson for GHK.

However, that the boson is massless here carries no significance. Higher corrections to this approximation move this mass away from zero. This need not be shown. It was and is common knowledge that masses (not constrained by the Goldstone theorem to be zero or by some special structure condition) must change order by order. The only issue was the Goldstone theorem and GHK showed that this did not apply in this case.

Furthermore GHK showed this is true in general in all gauge theories unlike the other papers which only considered an explicit model in the leading approximation.

Dr. Higgs starts with a seemingly different model. It is in fact identical when iterated. This was and still is well known. It is a property of renormalization in electrodynamics models. While Peter Higgs gives a non-zero mass in leading order approximation, it is not relevant. It is changed in higher orders and in fact cannot be determined from the theory which requires mass renormalization (because of infinities). This means the actual mass can only be determined by experiment. Note that even if this mass could be determined it has nothing to do with the physical "Higgs boson". The physical boson being looked for at the LHC comes from an identical mechanism but has the details of the interaction entirely different because the theory associated with the full Standard Model must be used. Arguments about Dr. Higgs having a Higgs particle because he writes his leading approximation with a mass are not correct. This has nothing to do with the actual mass in this simple model or the full Standard Model.

Physicists should know better than to make such an argument (and I am not saying you are making this argument) and if they do, they are either incompetent or purposely lying to confuse non-experts.

@Luboš: If we're gonna go down this line [for naming things fairly], we should go back all the way to P. Curie, who realized the role of symmetry: "It is dissymetry that creates the phenomenon", OEuvres (Gauthier-Villars, Paris, 1908). Some may say this is a bit disingenuous… maybe some will view this is a "semantics" argument, a typical "potAto/ potaHto" situation… but, in the end of the day, you have the following:

» Anderson never calculated this phenomena, at most he verbalized some arguments here and there. But, if things had been as simple as he made it sound (way back then), R.V. Lange would not have had so much trouble actually doing it [in cond-mat]. What Anderson never had to deal with was Goldstone's theorem, which was the whole point of all 1964 papers: evade the Goldstone theorem (in a time where the whole understanding of Gauge Theories as a theory of connections over certain Principal Bundles was not understood as it is today).

» Landau's approach is very different in spirit, in the sense that it does not remark on the fact that solutions to differential equations do not necessarily need to share their parents' symmetries. (I'm saying this because, eg, this is the whole history behind the GHK paper.)

In the end of the day, it is not difficult to follow, eg, Guralnik's history, from his PhD thesis to the GHK and Feldafing (linked above) papers. Comparing that context and history (acquired and inherited from Schwinger) with the other papers' and Anderson and Landau, etc… should make things fair and clear.

@Jester: to say that GHK swept stuff under the carpet, mildly or not, is not only disingenuous, it's flat out wrong. But somebody else already commented on the different approximation schemes used by the 3 different groups, and the 'anonymous' above already did a good job explaining most of the details in this case. So, i'll just say that maybe you'd do well to read those papers in detail, redoing those calculations in the context of those times, with the worries of those times (eg, evading the Goldstone theorem), with the prejudices of those times (eg, Heisenberg simply did not "believe" in symmetry breaking), etc, etc, etc.

The overarching theme of all this is called "Hermitian extension" and is present nowadays in very diverse topics, from PT-symmetric quantum mechanics to the recent analytic continuation of gauge theories. It's easy to learn this from such simple examples as the quantum mechanical square-well, by varying the limits of the well (cf Reed and Simon V2: no self-adjoint momentum operator for a free particle on the half-line). But i digress…

Dear Adam, I appreciate that gauge symmetries can't be broken. They're genuine redundancies identifying different points of the configuration space. The symmetry is just manifesting itself in a different way in the broken phase. One has to dress operators by the Higgs-dependent pieces to make it useful in the broken phase.

My adviser would be stressing this point constantly etc. And I agree that this is a difference from condensed matter physics because condensed matter physics never really works with fundamental gauge symmetries, except for the electromagnetic U(1) perhaps.

But the discovery of the difference is not really due to Higgs or his peers. It's due to other people who built particle physics. They created an infrastructure and when Higgs and others imported the Landau buttocks from condensed matter physics, it just automatically had the HEP properties it has, including exact gauge symmetries and Lorentz invariance. But exact gauge symmetries etc. were found by Yang, Mills etc. while Einstein is to be credited with the Lorentz symmetry (another naming paradox: Lorentz knew the transformations but didn't realize they formed a group etc. and of course that this group was related to Galileo's change of reference frames).

When I talk about the inspiration by condensed matter, I don't mean "just" superconductivity. I really mean Landau's general theory of second-order phase transitions (in thermodynamics). In Landau's CMT case, one just has free energy. It was the usual formula in which one may create a HEP system with an action similar to the free energy. And then we get models with the Higgs mechanism in HEP with all the extra purity - symmetries.

Someone mentioned Curie, I don't know whether this was a joke or not. Fine, things always have an even longer prehistory. But Landau had many of the same formulae, that's well beyond Curie's words.

Hey Adam, thanks for putting dots over i's very clearly, as usual. What matters is not just a discovery, what matters is realizing the importance of the discovery, insisting on it and driving the point home. Peter Higgs understood the importance of this new degree of freedom; others not. It was Higgs who published the PRD 1966 paper in which he developed in minute detail the Higgs boson theory, and in particular commented on the Higgs boson decay into two gauge bosons and - one of the modes in which it is being now discovered. This is a very modern paper which develops what is now known as the "Abelian Higgs model" - textbook stuff. GHK say that in their approximation Higgs boson is massless. It's OK. But I don't think they comment on the couplings of the Higgs boson to the massive gauge bosons. This means that their approximation just does not make it. They have seen a glimpse, but ignored it. Too bad, but that's life. Other examples are known. Khriplovich correctly computed asymptotic freedom in 1969, but he did not realize the importance and did not pursue it further.

Anonymous: "» Landau's approach is very different in spirit, in the sense that it does not remark on the fact that solutions to differential equations do not necessarily need to share their parents' symmetries."

I completely disagree with this assertion. Landau is, on the contrary, the #1 person among all the people who have ever lived on Earth who should be credited with this important observation that symmetries of the laws don't have to be shared by the solutions. That's what his general theory of 2nd order phase transitions is all about.

A magnet has no magnetization above the critical temperature. The order parameter is zero. Below the temperature, the free energy is still an even/symmetric function of the order parameter but the minima break it. And we know it from permanent magnets. It's disingenious to "criticize" Landau for not realizing this crucial point.

I wasn't refering to your comment, but to Jester post (and not really to Jester, which I'm sure already know all that, but to people who read this blog and don't really know about QFT. The point that I stressed is too often overlooked.)

I think you can have other gauge group in condensed matter, when you take the continuum limit of strange lattice theory, but as I said, people there call all symetry a gauge symetry...

Slava: "Hey Adam, thanks for putting dots over i's very clearly, as usual. What matters is not just a discovery, what matters is realizing the importance of the discovery, insisting on it and driving the point home. Peter Higgs understood the importance of this new degree of freedom; others not."

Fine, a totally legitimate attitude. And I almost fully agree with it.

By this very criterion and Higgs' own wording, it's then Anderson who should be credited with realizing and promoting the importance of the Goldstone (massless) scalar excitations.

"This phenomenon is just the relativistic analog of the plasmon phenomenon to which Anderson has drawn attention..."

Now, I would agree that Higgs wrote the first modern papers on the remaining massive Higgs boson. But this boson is still just a fraction of a theory, the "Higgs" mechanism, and a crediting problem is then that people talk about the "Higgs boson" more often then they talk about the BEH... mechanism, and then, logically, use the Higgs mechanism for the mechanism as well.

When one summarizes the results, the frequency of the name Higgs in all the discussions about the Higgs/BEH-mechanism-related processes is still vastly overstated relatively to others. Technically you may justify individual pieces of the common terminology and overlook the distortions it creates.

But when you look at the result as a whole, statistically, it's still obvious that the importance of Peter Higgs in the discovery of the Higgs mechanism and related things is overstated.

Dear Adam, when I say that you can't have gauge groups in condensed matter, except for U(1), I mean that gauge groups in a particular description never emerge spontaneously.

A gauge group is an identification of elements of the configuration space that must exist from the beginning, from the first moment when you define the theory.

If you create any system from atoms etc. that can actually be built in a condensed matter lab, it can only use the gauge symmetries that already exist in Nature - the SM or GUT gauge group - and it can never create a new one. In practice, U(1) electromagnetism is the only gauge group that survives.

If you create a lattice gauge theory with the QCD-like degrees of freedom composed of "condensed matter stuff", then the symmetry won't really be gauge and the degrees of freedom that would be unphysical in HEP theory with a genuine gauge symmetry won't be unphysical in the CM model. Incidentally, such a theory can't be relativistic; if it were relativistic, it would inevitably contain ghosts (timelike gauge bosons) in the physical spectrum.

ah, the glories of the Nobel prize and what their imminent scent does to honorable scientists...

it was BEH at Moriond simply because Englert was in the audience. and because BEH sounds silly, one speaker suggested EBH - or EHB?

whatever. that is just gearing up to which three physicists will get the invitation to Stockholm, nochting else.

Adam, you make an interesting and almost correct point. what you are forgetting however is that a global group is always a subgroup of a local one, so breaking SU(2)xU(1) global implies breaking the local group, too.

which, as you point out, can not and therefore does not happen as it is just a redundancy of our description of the gauge field. so really nothing gets broken in EWSB, the symmetry is just realized in a different way and there is an order parameter (the boson masses) to that transition. "symmetry breaking" is just a term that is historically motivated and debatable as the term "Higgs" for the scalar boson or the mechanism.

Chris, you write that a global symmetry can't be broken because it's a subgroup of the local one. (By the way, in quantum theories with Einstein-like gravity, it's probably needed for consistency to embed every global symmetry in a local one.)

However, I think you are overlooking a subtlety. Physical states must be invariant under local symmetries... but that's strictly speaking only a necessary condition for the local symmetry transformations that become trivial at infinity.

The global gauge symmetries that do nontrivially act on the asymptotic region of the spacetime don't have to keep the physical states invariant. This is really why we can have states with nonzero total electric charges or nonzero total ADM mass even though U(1)_em as well as diffeomorphisms are local symmetries.

what you say is formally correct, but i don't see the point (and the neutrality requirement for asymptotic states depends on the dynamics of the theory really - i.e. which phase it is in).

my statement was, that all descriptions with a certain Higgs vev that are related by the global part of the "broken" gauge symmetry are physically identical - i.e. the global symmetry is not really broken, too. would it really be broken the Goldstone theorem would apply and there would be a massless mode.

Dear Chris, I agree with you that some phases require the total charge to vanish but some don't.

My narrow point is what I wrote and I could only repeat it. My broader point is that due to this subtlety, the condensed-matter case and high-energy case are much closer to each other than some people in this thread try to suggest.

In particular, my point was also to disagree with your assertion that "all descriptions with a certain Higgs vev that are related by the global part of the "broken" gauge symmetry are physically identical - i.e. the global symmetry is not really broken, too."

It's just not necessarily the case because the global transformations don't vanish at infinity, so their generators don't have to annihilate the physical states.

Indeed, this has consequences for the existence of Goldstone bosons. The generic degrees of freedom produce Goldstone bosons in the bulk which manifest themselves as the longitudinal modes of W and Z bosons. It's ambiguous to say whether these particles arise from the excitations of the gauge fields or the Higgs doublet; it's really some function of them that become the longitudinal massive gauge bosons.

Indeed, the gauge character of the symmetry implies that the number of physical degrees of freedom is smaller than in a theory that would contain the gauge field and the Higgs doublet without any symmetry. But this only counts the bulk degrees of freedom.

If you want this "Goldstone litmus test" to answer the question whether the SU(2) x U(1) transformations that are *not* vanishing at infinity also have to preserve the states, you will have to find out whether there are additional "global" degrees of freedom of the massless Goldstone bosons that are not included in the longitudinal W/Z boson excitations.

This is a question you can't answer by local experiments. I choose to answer this question Yes, there exist these extra degrees of freedom at infinity: they're what allows one to switch between the superselection sectors with vevs that are related by the symmetry. These superselection sectors are equivalent because of the global symmetry inside the gauge symmetry but it's still legitimate and natural to say that they're not physically equivalent.

All these discussions are affected by the question what you mean by the global transformations and whether you include terms that depend on the gauge fields in them.

If you do include, as in the full theory, then you should say that charged particles in QED are really neutral because the charge from "rho_j" is compensated by "div D" - the whole difference "div D - rho" may be viewed as the generator of the local symmetry, and it's zero point-wise.

However, there's also an additional global symmetry that only acts on the phases of the charged (Dirac, ...) fields and doesn't subtract anything related to the gauge field and its divergence. This charge can obviously be nonzero, so this single symmetry is not "gauged" in the sense that everything must be an uncharged singlet. One has to distinguish the adjective "gauge" in the sense "with a parameter that is spacetime-dependent" and "gauge" in the sense of "we require the states to be invariant under it".

The Anonymous of <15 March 2012 02:29> must be the same "Mary at CERN" who, a few months ago, wanted to change the "Higgs boson" article in Wikipedia and insert paragraphs taken straight from Guralnik's reviews.

When I tried to explain to Mary how Wikipedia works, and why he/she shouldn't push the GHK point of view in the Wikipedia article without properly attributing Guraknik's statements, Mary brought forward the very same arguments of the Anonymous here, with *the very same sentences*, including the "physicsist should know better..." bit. See http://en.wikipedia.org/w/index.php?title=Talk:Higgs_boson&diff=454491389&oldid=454412414

Mary's campaign sort of collapsed when another review by Guralnik was posted on the arXiv, and I realized that Mary had been quoting from it before it had been made public: http://en.wikipedia.org/w/index.php?title=Talk:Higgs_boson&diff=455186338&oldid=455018393

Then it became obvious who the puppeteer was... I suspect that they are trying to pull the same trick here. "Mary" please, next time, if you want to stay anonymous, try at least to change the wording of your posts... ;-)

Luboš: regarding Landau, phase transitions, and symmetries of differential eqs… how far do you want to go down this particular rabbit role? All the way down to Galois? How many people have ever remarked on how the dynamics changes with flows in parameter space? Are you willing to throw Wilson/Renormalization with the bath water too?

I'm fine with the cliché 'we agree to disagree' — you're entitled to your opinions. But if we are to follow the facts in order to appropriately recognize everyone's contributions, we'll probably be here for a long time…

I want to go as far as necessary for the revelation of the genuine ideas that were ultimately used by Weinberg to write down the mechanism of spontaneous symmetry breaking in the Standard Model.

If you don't want to study the history and flows of ideas at all, the only legitimate term for the Higgs boson and Higgs mechanism, whenever we talk about the real world, would obviously be Weinberg boson and Weinberg mechanism.

There's no Abelian Higgs model in the current picture of particle physics so in your "strict" attitude avoiding the history, these are as irrelevant historical episodes as Galois.

Even more obviously, there's no Galois and RG flows in the reasons why the Higgs mechanism actually works. The Higgs mechanism even works at the classical level so why would you mention RG here? These are totally independent things. Application of RG on the Higgs mechanism (or anything else, for that matter) came after the Higgs mechanism.

One may choose different "philosophies" how deeply one wants to study and credit intellectual components of the BEH mechanism. But there's no internally self-consistent attitude to such things that could neglect Englert and others. This is not an academic or politically correct question. With all due respect to Peter Higgs, I think that Englert (as well as Nambu as well as Landau) has made a greater overall contribution to physics than Peter Higgs and the oversimplified crediting of the BEH mechanism to Peter Higgs is just a small part of the injustice.

Lubos, you don't get it. This particular Anonymous (which I suppose is the one of <15 March 2012 03:59>) does not seem to care much about the BE side of the BEH mechanism, not to mention Nambu or Landau. What he/she is trying to push - in concert with the other Anonymous ("Mary") of <15 March 2012 02:29> - is the idea that the GHK paper was somehow more complete than the earlier two (BE and H).

@MotlAll very good points. Higgs certainly gets too much credit over the other two 1964 PRL papers. In evaluating "credit" for the mechanism/boson one has to consider two points of order and quality.

It is a shame that “Nobel Math” prevents folks from viewing these 1964 PRL papers as a group. Clearly, one was earlier (BE) and one was more complete (GHK) than others. However as a group, these three papers really shaped how the mechanism and boson was viewed and supported the Standard Model.

The discussion of symmetry breaking and how gauge symmetries are never truly broken is interesting to me. Can someone please recommend a text to help me learn more about this, preferably at roughly a first or second year grad student level?

Ptrslv72: I truly fail to understand the value of your comments above. While on the Wikipedia discussion page they may have their weight (given Wikipedia's purpose and their clearly stated guidelines), here they are as close to meaningless as possible. And the reason is simple: Wikipedia is not a place to discuss the merits of technical aspects, but this is not the case here where the discussion is explicitly about the Physics.

In this very clear context, your comments here are nothing but smear tactics: discrediting Anonymous/Mary on the basis of anything other than the content of the posts.

Further, you showed how completely unaware you are about how science actually works. Contrary to some people's beliefs, scientists do share preprints and articles before they are published. It is also frequently the case that these get shared even more. So, your attempts to conclude that there exists a puppeteer or a puppet or plagiarism or ctrl-c—ctrl-v or whatever else… are simply unfounded.

In the end of the day, it is because of examples such as this one that it becomes impossible to have a meaningful conversation on topics which should not be this controversial (the Physics is pretty clear otherwise).

(1) Let me try to keep the focus very clear, since you seemed to have delved into a completely different direction than what I had in mind. I mentioned a range from Galois to Wilson to remind you that historically many folks have tried to deal with the solution space of [systems of] differential equations and how it changes when the parameters change.

(2) Far from me to say anything negative about Landau: I have learned a lot from his books, articles and sheer legacy. That was never my intention. So, please, do not take the discussion in that direction.

(3) I just did read your post on this subject: well done! Let me just say this (and I do not mean this to be a cross-post against your post — that's just poor form): just like there was a lot of Physics developed behind the "iron curtain" that did not quite leak to other parts of the globe, the converse is also true (there was an amount of physics that did not make it through the curtain in the other direction either). Schwinger, Gilbert, etc, etc, etc… they had a history of probing this same question, independently of other folks. And this was the main point.

Personally, I truly appreciate the new 'status' that the Internet brings to cases such as this: now we can just track most of this information on Wikipedia, and make sure to always acknowledge appropriately. Unfortunately, this has not always been the case… and this is the point where we all find ourselves here.

I hope to have been clearer and that, as such, you understand me better this time around.

"I mentioned a range from Galois to Wilson to remind you that historically many folks have tried to deal with the solution space of [systems of] differential equations and how it changes when the parameters change."

I understood this intent of yours; it's just not quite clear to me that the research topic you described is equivalent to the Higgs mechanism in any sense.

Good you clarified the things about Landau etc.

I doubt you're right that science such as physics sometimes didn't get to the socialist bloc. There was no barrier of this kind. In particular, in the Soviet Union, they stole all copyrights and translated every conceivable book and article into Russian.

Moreover, when I talk about the USSR in this familiar way, it's partly a comical exaggeration. Czechoslovakia has never been *that* close to the Soviet Union, we were in between not only in the geographic sense, so if there were different influences in the West and in the East, we would be exposed to both sides approximately equally. It's really not my intent to give a better treatment to Russians because they're Russian or something like that. Despite Landau's breadth and great achievements, I still think that only a very small portion of scientific progress was created in Russia. But constructing internal-symmetry-preserving equations/laws that have interesting asymmetric solutions (that may be studied with quite some detail) is exactly one of the few memes whose first discovery I would attribute to a Russian.

Right, the Internet brings new things to the propagation of ideas and science etc. Some of them are good, some of them less so.

"when I say that you can't have gauge groups in condensed matter, except for U(1), I mean that gauge groups in a particular description never emerge spontaneously.[...]If you create any system from atoms etc. that can actually be built in a condensed matter lab, it can only use the gauge symmetries that already exist in Nature - the SM or GUT gauge group - and it can never create a new one. "

I think you're wrong on that point. You can have different gauge symmetries in CM (even U(1) symmetries different from U(1)_EM) in the low energy limit of CM models. These symmetries are obviously not fundamental, but are emergent symetries arising from constraints and never the less have physical implications.

@ chris :"what you are forgetting however is that a global group is always a subgroup of a local one, so breaking SU(2)xU(1) global implies breaking the local group, too."

That does not mean that I can't have a gauge group H_l ad a second global group H_g. The symmetry groups are H_lxH_g. you can break H_l, but never H_g.

"so really nothing gets broken in EWSB, the symmetry is just realized in a different way and there is an order parameter (the boson masses) to that transition."I don't agree with you. The vev of the Higgs clearly breaks the global symmetry (in the U(1) equivalent, you choose a given phase for the order parameter, which is not invariant under a U(1) transformation). Nevertheless, there is no Goldstone mode, because when you expand your field around the vev, the transverse mode (of the Higgs field) is 'eaten' by the gauge field. The global (broken) U(1) symmetry just change which component of the bosonic field is the eaten Goldstone or the Higgs mode.

the Wikipedia story is relevant to this thread as it puts in proper context the campaign that you and "Mary" are leading here. And the fact that the whole comment of <15 March 2012 02:29> was in fact cut and pasted from a Wikipedia talk page dating from months ago seems sufficiently bizarre and noteworthy to me. I can understand that you find the whole story embarrassing and you'd rather not have it aired, but that's your problem.

As to the preprint, believe me, I know a thing or two about how science works: quoting other people's words without attribution and pretending that they are your own is not acceptable behavior in any discussion. And in that particular case, the fact that "Mary" had access to unpublished stuff highlighted his/her possible conflict of interest (which is a big no-no in Wikipedia).

Either "Mary" is piloted by Guralnik, or she is an overzealous admirer who's doing a rather bad service to her hero.

(1) I understand the overall theme of your complaint (non-attribution, ctrl-c—ctrl-v, etc) and i don't even disagree — specially in the Wikipedia setting.

(2) At this point, i'm sure you can tell when you're talking to "Mary" and when you're talking to other people. So, why pretend?

(3) With that out of the way, let me be *very* clear: "What 'campaign' do you think *I* am waging here?" But, please, don't hide behind your implied ad hominems, and add some value to your response by doing a fisking of the Physics involved. Maybe you could even read Lubos post on this topic — that's an idea. You have to be able to appreciate the irony, the 'meta', in this situation, non: you and Mary performing the exact same actions, except in different polarizations (if you will). The tragicomedy of life…

» So, summarizing: No, i'm not "Mary", and am not embarrassed by anything that i've said or done (ergo, i have no "problems" to deal with in this regard). This is, at least, the second time i personally ask you to 'fisk the Physics' and not to resort to personal attacks (veiled as they may be). So, if all you can do is attack Mary's poor manners (netiquette), we won't have much more to talk. On the other hand, if you'd like to venture into the Physics and try and *understand* what several people have been saying for quite some time now… please, be my guest: i'd be pleased to engage in such a discussion.

- where did I imply that you and "Mary" are the same person? As you may easily check, I always took care to specify which "Anonymous" I was referring to. "Mary" is surely the Anonymous of <15 March 2012 02:29>, and perhaps (but that's not particularly relevant) the Anonymous of the first two comments. However, while we are all clear that you are not "Mary", will you also state that you are not (and have never been) communicating with her? (If you know who she is, BTW, you should try to explain to her that she's damaging her own cause).

- while we are at it, would you care to elucidate how and why I would be "performing exactly the same actions" as Mary?

- as to which "campaign" the two of you are waging (together or apart, but seemingly based on the same sources), it is simply the one I mentioned in my comment of <15 March 2012 16:48>, which you (unwittingly, I suppose, due to the moderation block) confirmed in the very next comment addressed to Motl. BTW, I couldn't help smiling at the radical change in your attitude towards Motl after you read his blog post...

- as to "The Physics", it might come as a surprise to you that I'm not particularly excited about who exactly understood what 48 years ago. There already has been some pretty good "fisking" in Jester's post and in this thread, and I am sure that Englert's or Higgs' versions of the same story would be equally illuminating but probably rather different. What irks me are manipulation and not-so-hidden agendas, and that's what I found appropriate to point out.

On the bright side, look how far you've sank this discussion? We got to the point where you're irked by other people's actions, but not by yours. Reasonable as this may be, it's exactly the 'meta' i mentioned before: her campaign, your campaign, potAto, potaHto… i forgot, please, remind me again: who elected you referee in this game? I'd be more than happy to vote for you if you had ever made a single point about the physics. But, alas, all you seem to do is deflect the physics and politicize the situation. Which, as you argued, seems to be Mary's actions, to your eyes. So, cut from the same cloth, are we…? (Don't worry, though, people who know this field understand perfectly well who's the source for your line of argumentation. This game goes both ways and just because one side refuses to be political, it doesn't mean one does not understand what's happening.)

Thumbs up to ptrslv for unmasking the campaign by Mary "Guralnik", on wikipedia and here, to claim retroactively that GHK understood the Higgs boson. If they did, they would have computed its mass, which takes two seconds if you realize the importance of this extra degree of freedom. Respective approximations, my m-ass.

thanks for the thumbs-up. The surreal bit is how these guys come down here and on Wikipedia like an army of clones, backing each other up with Guralnik's reviews, and I'm the one who's being political (and has no clothes, whatever that's supposed to mean) for pointing it out. BTW I'm still waiting to learn who's "the source of my line of argumentation", I should at least get a beer from him/her...

@Anon:More precisely, the phrase allegedly added in response to the referee is the one about "prediction of incomplete multiplets" at the end of the paper. But Eq. (2b) and its interpretation in the following paragraph must have been there from the start.

So much text so little content. I have been monitoring this blog “evolve” to this and now feel compelled to post. I don't know any of the people you are fingering in your complaints – Mary, Anon X, or Gurnick. However the posts you have the issues with are some of the few here that have actual physics content.

None of the "Mary" or "Anon" posts are contested on the actual physics. Is there any actual physics (not manners or politics – I align with your points here) do you not agree with? Are you a physicist? …On the PRL referee notes, according the University of Edinburgh, after Nambu’s review, Higgs' revised paper drew attention to the possibility of a massive spin-zero boson in its final paragraph.

It is fairly obvious who Anon <16 March 2012 18:01> is talking about (below) when he refers to "source for your line of argumentation."

However, just as I am pretty sure Guralnik is not directly behind these individual posts, I am just as confident Ptrslv72’s posts are not directly supported by this other person – or "source" (@Ptrslv72, so no worries)

===============================“(Don't worry, though, people who know this field understand perfectly well who's the source for your line of argumentation. This game goes both ways and just because one side refuses to be political, it doesn't mean one does not understand what's happening.)”===============================

I'd like to second the call for a good introduction to the modern understanding of gauge symmetry breaking (or not-breaking, as the case may be). What is the sense in which gauge symmetry is not broken, if the Higgs vev, <0|H|0>, is non-zero, and is not a gauge-invariant object?

Yes, I am a physicist, and as a matter of fact I've even done some work on the Higgs boson. As you can guess from my nickname, however, I wasn't around in the Sixties, and what I know about the topic I learned it from a modern perspective. Thus, I don't think I'm more qualified than anybody else around here to assess the relative merits of the 1964 papers, nor, as I already mentioned, am I particularly excited by the issue of who understood what 48 years ago. In fact, my interest for "Mary" and her "campaign" started only when she tried to sneak Guralnik's POV into the Wikipedia articles without proper attribution. Then I was amused at seeing whole chunks of the same stuff being robotically pasted here, and I found it useful to point it out (only to earn accusations of "smear tactics").

But you write that you "align" with that part, so let's move on. Do you really want to know what I think of Mary's arguments? I think they are a smokescreen. In his paper, Higgs identifies the boson mass as the second derivative of the scalar potential evaluated at the minimum, while in the GHK paper the boson is massless. Mary's main point appears to be that, since the quantum corrections to the scalar potential change the boson mass, the fact that Higgs mentions the boson mass in the classical theory is irrelevant. This, in her mind, implies that GHK "had the boson" just as Higgs did.

Now, we can even leave aside some facts that look obvious from our modern perspective, i.e. i) that the boson mass is a free parameter even in the classical theory (Mary should have known that it's not just because of quantum corrections that "experimentalists did not know for sure where to look for the particle") and ii) that the boson mass is the second derivative of the scalar potential even after the theory is renormalized and the quantum corrections are included in the potential (only under the approximation of neglecting the external momentum in the boson self-energy, but I doubt that this is what Mary had in mind).

The reason why it's all a smokescreen is that this issue of quantum corrections to the boson mass does not change one iota in the accuracy of the "swept under the carpet" comment in the original post by Jester, i.e. the comment that triggered the attack of the clones. As Mary herself teaches us, GHK's attention was focused on showing how the Goldstone theorem is avoided. And indeed it looks like, when they found a seemingly massless boson in their model, all they cared about was to stress that it's not a Goldstone boson (hence, I suppose, the "completely decoupled from the massive excitations" bit, which might sound even more damaging than the "massless" bit). They did not seem to realize, as Higgs did in his paper, that the additional boson is in fact "an essential feature of the theory". Indeed, while Higgs went on developing his Abelian model (and discussing the Higgs-gauge boson coupling) in the 1966 paper, Guralnik repeated the very same statements from the GHK paper in his own longer paper of 1965 - the one linked by the other Anonymous at the beginning of the thread. If Guralnik had understood the importance of the extra particle, that would have been a good opportunity to elaborate on it.

Now that I yielded to popular demand and wasted time repeating obvious stuff that was already mentioned by others (Jester, Slava) in this thread, is anyone the wiser? I don't think so, and I certainly have no inclination to start debating the arcane points of 48-years-old papers with Mary and the other anonymous Guralink clones.

i don't want to drag this out endlessly, but just try to think a bit about what you mean by "eaten". it's so often said so easily - this goldstone mode never existed to begin with. it's not as if a gauge boson would decide to "eat" the mode ater it has broken a symmetry ^_^.

the higgs vev does not break any symmetry. yes, in a particular gauge it has a particular value - but so what? what is the physical observable that gives the phase of the vev? if you can't name any it's obviously a redundancy of your description and not a true symmetry that go "broken". that's all.

same is true by the way for the "anomalous breaking" of U(1). no symmetry ever gets broken by the anomaly because if it is anomalous, there never was a symmetry to begin with. don't get fooled by terminology.

Chris, you are wrong. The Higgs VEV breaks the global subgroup of the gauge symmetry (a point first emphasized by Elitzur, I think). Its direction in internal space at any one point in space is obviously a matter of arbitrary convention, but the difference between the directions it takes at difference points in space can be described in a gauge-invariant way and gives rise to physically observable consequences. Look up "Kibble mechanism".

What to call the particle formerly known as Higgs 18:00 20 March 2012 by Valerie Jamieson http://www.newscientist.com/article/dn21604-what-to-call-the-particle-formerly-known-as-higgs.html

A rose by any other name might smell as sweet, but does it matter what a subatomic particle is called?

Earlier this month, organisers of a physics meeting requested that the Higgs boson – the still-hypothetical particle thought to endow other particles with mass – instead be referred to as either the BEH or scalar boson. The name change might seem esoteric, but it hints at a complex past – and trouble ahead over credit for the boson, if it is found.

To understand, rewind about 50 years. As with most scientific advances, a single mind did not solve the mass puzzle. Work by Yoichiro Nambu of the University of Chicago in 1961 led to the idea that a mass-giving field interrupted an early universe until then filled only with massless particles.

In August 1964, Robert Brout and François Englert (the B and E in BEH) at the Free University in Brussels, Belgium, ironed out some kinks in the theory and detailed a mechanism. But it was Peter Higgs at the University of Edinburgh, UK, who first explicitly predicted the particle we now call the Higgs – in a paper published in October 1964.

This progression explains the BEH boson option, one of the two mooted at the annual Moriond meeting in La Thuile, Italy, but why change it this year? Many say it is because Englert was at Moriond, and the organisers didn't want to upset him. Other attendees, however, were upset by the proposed change, including Wade Fisher of Michigan State University in East Lansing.

Anonymous scalarFisher says the debaters fall into four main camps: Higgs supporters; BEH proponents; those favouring the anonymous scalar boson; and those who favour another name – the BEHHGK boson. The latter group, including Fisher, want to credit Dick Hagen, Gerald Guralnik and Tom Kibble, who published a mass-giving mechanism in 1964.

Some believe that these physicists do not deserve to be considered on an equal footing with Brout, Englert and Higgs because their paper appeared later. Others disagree, because the paper was received by the journal Physical Review Letters before Higgs's paper was actually published. Guralnik has even written a paper recalling how he heard of Brout, Englert and Higgs's papers just as he and his colleagues were about to place their manuscript in the envelope. "Not a single thought or calculation was removed or added," writes Guralnik. The only change they made was to the references, something that he now bitterly regrets.

The omission of these three names from the BEH name chosen at Moriond "was considered a curiosity, a slight, a political statement and a mistake by those to whom I spoke", says Fisher.

Higgs momentumOthers point to the ad-hoc way in which particles seem to be named. "It's not like elements whose names are very carefully chosen by a committee," says physics Nobel laureate Steven Weinberg at the University of Texas at Austin, who named the Z boson that carries the weak force.

This might be a taste of the debate awaiting a Nobel prize committee soon. Many are calling 2012 "the year of the Higgs" – but a Nobel prize can be split between no more than three people (Brout is out of the running as he died last year).

In the meantime, will BEH catch on? Fisher doubts it. "There is too much momentum behind the name 'Higgs'," he says. "The Nobel committee may decide otherwise but they are not the sole arbiters of historical accuracy."

As physicists close in on the Higgs boson, they should resist calls to change its name.

The naming of the Higgs boson as such is clearly a simplification — physicists besides Peter Higgs contributed to the theory that predicts it. But it is far from the most extreme example.

The relationship between the velocity of recession of galaxies and their distance from Earth that we call Hubble's law was first formulated by Belgian cosmologist Georges Lemaître. The quantity known as Avogadro's number was first calculated by Austrian chemist Johann Josef Loschmidt. Higgs, a physicist at the University of Edinburgh, UK, at least has the strongest claim to credit for the boson. And for the arcane world of particle physics, simplification is often a good thing.

In 1964, Higgs was the first to postulate the existence of a massive particle arising from the mechanism of electroweak symmetry breaking, in which a unification of electromagnetism and the weak nuclear force fails in such a way as to give some force-carrying particles masses while others remain without. Yet moves are afoot to rename the Higgs. Earlier this month, some speakers at the Moriond particle-physics conference in La Thuille, Italy, chose to describe progress on the search for the BEH scalar boson (after the physicists Robert Brout, François Englert and Higgs) or the SM scalar boson (where SM stands for standard model).

It is not hard to guess why. Experiments at the Large Hadron Collider at CERN, Europe's premier particle-physics laboratory near Geneva in Switzerland, have reported tentative signals of the Higgs. If these are real, data collected in 2012 should see CERN claim a discovery. A Nobel prize is in the offing, and one that should arguably go not just to the experimentalists, but also to the theorists whose efforts inspired the successful search. But who — besides Higgs — should be included?

The name Higgs boson was supposedly coined by Korean-born physicist Ben Lee, some time between 1966 and 1972. According to journalist Ian Sample, Lee learned about the mass-giving mechanism from Higgs, and later coined the term as a shorthand. Yet several others played an important part in developing the theory that gives rise to the Higgs.

Belgian physicists Brout and Englert were the first to publish on the subject in 1964, building on ideas from condensed-matter physics developed by physics Nobel laureate Phil Anderson and others. Higgs published the same year; his paper contains the first mention of the boson. Tom Kibble, Gerald Guralnik and Carl Hagen followed with a third account that is generally considered more complete. One interpretation of this history is reflected in the American Physical Society's joint award, in 2010, of the J. J. Sakurai Prize for Theoretical Particle Physics to Brout, Englert, Higgs, Guralnik, Hagen and Kibble.

This provides plenty for physicists to argue about. In 2010, a row over credit erupted when Brout, Englert and Higgs were acknowledged in an advertisement for a conference on the particle but Guralnik, Hagen and Kibble were not (see Nature http://doi.org/ctz988; 2010). Meanwhile, 2011 saw a dispute over editing of the Wikipedia article 'Higgs boson' between one editor who supported Guralnik's view that his paper with Hagen and Kibble proposed a boson and another who was pro-Higgs.

Particle physicists should not rename the Higgs. And the reason would be obvious to anyone in business: branding. There are already relatively few concepts in their subject that have achieved widespread recognition without crossing one of them out. In business, it would be considered destructive to take a well-known name and replace it with a long-winded, technical-sounding alternative that no one has heard of.

Correct allocation of credit is important, and authoritative accounts of the history of science are useful and enlightening, but both must be balanced with science's need for consistent conventions, brevity, and public communication and outreach, especially when taxpayer's expenditures, such as the US$6.5 billion for the Large Hadron Collider, are at stake. Renaming the Higgs boson in the year when it is most likely to be found gets the balance wrong. (And anyway, Higgs is a better name than the God particle, isn't it?)

Physicists working at the Large Hadron Collider at Cern are now engaged in a strenuous search for a particle of a new type, known as a Higgs boson. Much more is at stake in this search than the effort to add one more item to the quarks, electrons, and so on that make up the menu of known elementary particle types.

This is because the discovery of the Higgs boson would confirm a theory of how the symmetry between two of the fundamental forces of nature became broken, and how elementary particles get their masses. Not discovering it would be even more exciting, putting us back to work to understand all this. To explain what is at stake here, I first have to say something about what physicists mean by symmetries, and by symmetry breaking.

A symmetry of the laws of nature is a statement that the laws remain the same when we change our point of view incertain definite ways. A large part of the physics of the 20th century was devoted to the discovery of such symmetries. It started in 1905, when Einstein in his SpecialTheory of Relativity declared that allphysical laws, including those that dictate the speed of light, remain the same when we change our point of view by viewing nature from a moving laboratory.

But the symmetries of the laws of nature are not limited to changes in the way we view space and time, as in Special Relativity. The laws of nature may also be unchanged when we replace various types of particles in our equations with other types of particles. For instance, there are two kinds of particles that make up atomic nuclei: protons and neutrons. In the 1930s it was discovered that the laws that govern the strong forces that hold these particles together in nuclei do not change their form if we replace protons with neutrons, or even replace protons (and neutrons) with a mixture, that might for example be 30 per cent proton (or neutron) and 70 per cent neutron (or proton).

It’s not that physicists in the 1930s knew the laws governing the strong nuclear force. The importance of symmetries is that we can learn about them from experiment, and use them to make new experimental predictions, even if we do not know the laws to which they apply.

For instance, even not knowing the nature of nuclear forces, physicists could infer from the proton-neutron symmetry that the energy of the lowest energy states of the nuclei of boron 12 and nitrogen 12 should be the same. It should also be the same as the energy of one of the excited states of carbon 12, because these three states can be converted into each other by changing protons and neutrons into mixtures of protons and neutrons. Symmetries are often invaluable clues to what is going on at a more fundamental level than we can otherwise approach.

In the early 1960s, theoretical physicists became excited by a new idea, that opened up the possibility that nature may obey a richer variety of symmetries than had previously been imagined. The idea was that the laws of nature, expressed as mathematical equations, might have symmetries that are not respected by physical phenomena, represented by solutions of these equations. In such cases, we say that the symmetries are broken—they may be exact properties of the laws of nature, but they are not immediately apparent in physical phenomena.

Broken symmetries do have physical consequences, just not easily-spotted consequences like those of the neutron-proton symmetry, which put physical particles or nuclear states in families of the same energy. In 1962 a theorem was proved by Jeffrey Goldstone, the late Abdus Salam, and myself, following earlier suggestions of Goldstone and Yoichiro Nambu, that deduced what seemed like a general consequence of broken symmetries. This theorem states that in any theory in which a symmetry like the proton-neutron symmetry is broken, there must exist particles with no mass or spin. Such new particles of zero mass were not known, and would not have escaped detection, because no minimum energy is required to create them, so this seemed to close off the possibility that nature actually obeys any broken symmetries.

The gloom lifted in 1964, when three groups of theorists independently pointed out an exception to our theorem. They were, in alphabetical order, Robert Brout and François Englert; Gerald Guralnik, Richard Hagen, and Thomas Kibble; and Peter Higgs (BEGHKH). They pointed out that the theorem of Goldstone and the others does not apply for a certain class of symmetries, known as local symmetries. For these symmetries, the transformations that leave the laws of nature unchanged can vary from point to point in space and time. To keep the equations unchanged under such transformations, theories with local symmetries must contain particles with zero mass and a certain definite amount of spin, equal to Planck’s constant.

The particle of light, the photon, is one such spinning massless particle. A large class of possible new local symmetries had been described a decade earlier by Chen-Ning Yang and Robert Mills, but these Yang-Mills theories had not yet found any application in realistic physical theories. What BEGHKH showed is that when a local symmetry is broken, the massless particles found by Goldstone et al are not realised as physical particles, but instead go to give mass to what would otherwise be the spinning massless particles of Yang and Mills.

None of the papers of BEGHKH proposed any specific realistic theory of particles and forces. In 1967 I was trying to work out a theory of the strong nuclear force, based on a broken local symmetry, without much success. At some point, I realised that I had been trying to apply good ideas in the wrong place. The right application was to the weak nuclear force, the force that allows a proton in a radioactive nucleus to turn into a neutron, or vice versa. The resulting theory turned out to be not just a theory of weak nuclear forces, but also of electromagnetism: the electroweak theory. That was of course very exciting. A little later pretty much the same theory was independently developed by Salam. Also, I found that Sheldon Glashow had explored this sort of theory, but without incorporating broken symmetry or Higgs bosons.

In the theory Salam and I developed, there is a local “electroweak” symmetry that if unbroken would require electrons, quarks, and the particles that carry the weak forces all to have zero mass. In the original version of this theory, there is also a quartet of fields, which would have zero values in empty space if the symmetry were unbroken. (Fields of this general type had already appeared in illustrative examples of local symmetry breaking presented by BEGHKH.) The electroweak symmetry is broken by the appearance of a non-zero empty-space value for one of these four fields. As a result, electrons, quarks, and the particles that carry the weak nuclear forces all acquire masses. Just one of the four spinless fields is manifested in this theory as a physical particle, an electrically neutral spinless particle, with interactions predicted by the theory but unfortunately with an unknown mass. This is the Higgs boson now being sought at Cern.

By now there is plenty of experimental evidence that nature really does have a broken local electroweak symmetry. New weak forces required by the theory were discovered at Cern in 1973. In 1984 the massive particles that carry the weak nuclear force were discovered, also at Cern, in both cases with just the properties predicted by the broken symmetry. What is not so clear is that the electroweak symmetry is broken in the way Salam and I described.

Beyond the Higgs

There are other possibilities. The symmetry may be broken by several quartets of spinless fields, in which case there would be several Higgs bosons, with complicated properties. A more radical possibility was suggested independently by Leonard Susskind and myself: the equations of the theory may involve no spinless fields at all. Instead, in addition to the known electroweak and strong nuclear forces, there would have to be even stronger “technicolour” forces, carried by particles that interact with the particles that carry the weak forces, and thereby break the electroweak symmetry. In this sort of theory there would be no Higgs bosons at all, but rather a whole zoo of new particles held together by the technicolour forces. One way or another, experiments at the Large Hadron Collider are going to settle the great outstanding question, of what breaks the electroweak symmetry and gives elementary particles their masses.

Important as that will be, even more exciting things may be discovered at the Large Hadron Collider. Astronomers have by now found several pieces of independent evidence showing that about five sixths of the mass of the universe consists of some sort of exotic “dark matter,” which is the dominant source of the gravitational fields of galaxies and clusters of galaxies, but otherwise interacts little if at all with ordinary matter. None of the particles in our present standard model of elementary particles (including the electroweak and strong nuclear forces) have the right properties to be the particles of dark matter. As one might have expected, various theorists have come up with various possible generalisations of the standard model, which contain candidates for the particles that make up dark matter.

Among the most promising of these candidates are WIMPs, or weakly interacting massive particles. These are particles that are individually stable, or at least can survive for billions of years, but that can annihilate each other in pairs, their energy turning into ordinary particles. The idea is that in the hot dense conditions of the early universe they would have been continually created and annihilated in pairs, until the expansion of the universe thinned them out so much that they could no longer find each other to annihilate.

We could calculate how many of these particles would survive to the present, if we knew their mass and how readily they annihilate each other. Or to put it another way, if we assume that these WIMPs make up the dark matter, and make a reasonable guess about how they annihilate each other, then we can calculate their mass. The so-called “WIMP miracle” is that their mass turns out to lie in the range of 10 to 100 times the mass of the proton, well within the range of masses that can be created at the Large Hadron Collider. So experiments at Cern may tell us what most of the universe is made of.

"So the Nobel prize should go to the referee".What a stupid reason. Referees cannot claim any authorship on a published paper. Their suggestions are only a natural part of peer to peer process, and the author if fully authorized to take advantage of them.

The article on the Higgs boson [“What’s the matter with Higgs? We may soon find out,” April 3] reveals an inadequate knowledge of history in according Peter Higgs full credit for the relevant theory.

In 1964, three papers appeared within a month that described the mechanism by which the spontaneous breaking of the electroweak symmetry gives mass to the gauge mesons. The first paper by Robert Brout and Francois Englert was quickly followed by one by Higgs and then another by Gerald Guralnik, Richard Hagen and Tom Kibble.

The last one is universally accepted as the most rigorous and complete.

About Résonaances

Résonaances is a particle physics blog from Paris. It's about the latest news and gossips in particle physics and astrophysics. The main goal is to make you laugh; if it makes you think too, that's entirely on your own responsibility...